What is the Mistake in Determining the Speed of Gear Rack E?

[sami23]

Homework Statement

The wheel is rigidly attached to gear A, which is in mesh with gear racks D and E. If D has a velocity of v_D = 5 ft/s to the right and wheel rolls on track C without slipping, determine the speed of gear rack E. Set r = 1.4 ft.

Homework Equations

angular velocity of gear $$\omega$$= v_D / r_D/IC
v_E = $$\omega$$ * r_E/IC

where r_D/IC = (1.4 + 0.75) = 2.15 ft
and r_E/IC = 0.75 ft

The Attempt at a Solution

$$\omega$$ = 5 / 2.15 = 2.3256 rad/s
v_E = 2.3256 * 0.75 = 1.744 ft/s to the left but it's wrong

What did I do wrong? Please help

 

[tiny-tim]

hi sami23!

… and r_E/IC = 0.75 ft

why 0.75 ?

(btw, what does "IC" mean?)

 

[sami23]

IC means the instantaneous center of zero velocity where the general formula is: velocity of a point = angular velocity of the body (cross product) distance of the point relative to the IC for a body having general plane motion (doing translation and rotation).

The distance shown in the picture from the center Point O to the track C = 0.75

My mistake... r_E/IC = 1.4 - 0.75 = 0.65 ft